 So, with regard to solutions in this week's lab, thank you, you say would you want to show a center line over here or not, yes sir, no sir, why sir, why not sir, yes or no. So, those who are yes and those who are convinced raise your hands, those who are no and those who are convinced raise your hands, the number of hands do not match the decibel level of yes and no. Maybe it will be a nice idea to show the center line over here, maybe, because if you do not show the center line there, then if you look at the top, it gives the impression that you have a rectangular slot or trapezoidal slot in there, if you do not show the center line. So, that is one thing, corrected figure from last lecture, so one of the ribs is smaller in dimension and then you see the fourth circle at the center, so we will start off fresh with perspective views, those are again a kind of pictorial views, those who are into art will love the next three lectures and those who are not into art will become artists, if you follow this, what those who are into art will like these three lectures including today's and those who are not into art will become artists, hopefully. Stay with me, some examples, spare your wow for some time, some examples, what you reckon are these lines parallel to each other, are these lines parallel to each other, yes sir, no sir, yes, no, they are parallel to each other, but you get the impression by looking at this picture that they tend to converge to a single point, they tend to converge, are these lines parallel to each other, again you get the same impression that they tend to converge, this is art, look at those rods on the roof, are these parallel to each other, but the impression that you get is, I will tell you a little story about this, I will tell you a little story about this, this is something that I worked on back in 1995, when many of you guys were probably 1 year old toddlers essentially or may not have been born, then I did not know how to draw a perspective, frankly I did not know how to draw a perspective, so this was just out of intuition, can you spot me, let most, so, but I do not want you guys to have the same feeling, so if you want to attempt something like this, I would want to make sure that you guys know how to draw perspective views, this is a different example, yet another example, let us go back to the first example, look at these parallel lines, they tend to converge to a single point, choose a line they tend to converge to a single point, this example, choose a line again the same thing, again the same thing, here the story is a little different, focus on the lines on the right of this vertical edge, focus on the lines on the right of this edge and any line you choose and you extend they tend to converge to a point on the right, likewise lines on the left of that edge, any line you choose tend to converge to the point or to a point on the left, what is interesting is that this point here and that point over there, they happen to lie on a horizontal, that is what is interesting, I call the point on the left as the vanishing point, point where all the edges tend to converge, point on the right as another vanishing point, I call the horizontal line as the horizon line, line of horizon and it is this line that separates the sky from the ground, something very similar, look at the edges on the right of this vertical edge and the edges on the left of that vertical edge, they tend to converge to two different respective points, which lie on the horizontal, again the points are V p 1 and V p 2 vanishing point 1 and vanishing point 2, line in red is the horizon line that separates the sky from the ground, in this case you have a single vanishing point, single point where all lines they tend to converge, lies on the horizontal which separates the sky from the ground and this point here I call it V p 1, this is again a horizon line, this is where possibly you are stationed as an observer and I call that or I call your position as the station point. Now, let us try to apply those rules in perspective projections, apply those observations in perspective projections, of course you know about views front view, top view, profile view, so this would what be the scenario in top view, let us say you have got a picture plane, just behind it let us say you have a cube placed in the top view again, this is where you are stationed, mind you we are working with top view, so this is where you are stationed, so imagine if a bird is looking at you as well as the object over there, so this is what the bird is going to be observing that you are looking at four vertices of the object like this, so those rays from the vertices will hit your eye in these directions from the top, so in a sense you happen to get the sight information from the top view, once again you happen to get the sight information from the top view. Now, let us switch back to the front view of the profile view, I am standing on some line or you are standing on some line that is called the ground line reference line, let us imagine that the object is on the same line as where I am standing and of course this is true height of the object, now notice something important at this point over there is the station point which actually belongs to top view, not the front view or the top view, in a sense in the front view you will be stationed here on the ground line, so this guy belongs to the top view that is something that you need to keep in mind, get the height in the front view what would be the horizon line for me, what would be the line of horizon for me in the front view, I am standing here this is my ground line, the line that separates the sky from the ground what would that be, would that be below my eye above my eye or at the level of my eye, level of my eye, so in the front view my eye will be here on this line right above the station point. And if I look very far off I will be seeing the vanishing points on this line, the left or on the right any vanishing point has to be on the horizon line, in the front view or the profile view you get the height information, now what you want to do is you would want to combine both views together, so you have components from the top view the object in the top view the picture plane, this belongs to the profile view of the front view, ground line to the profile view of the front view this station point belongs to the top view. So, what you have done is you have combined information from both views and place them together, now stay with me here. If I look at an object very far away in the front view, if I look at an object very far away parallel to this edge where would my vanishing point be, once again if I look at an object very far away from me, but along this direction where would my vanishing point be, where would that be, bottom right I am looking straight, I am looking straight and parallel to may be one of those edges. Of course, my vanishing point will be on the horizon line and along this direction which is going to be where, that is my vanishing point. So, to draw a perspective in summary you have to identify the picture plane, you have to identify how the object is placed with respect to the picture plane, where you are stationed in the top view, in the front view you have to identify the ground line, you have to get the profile view of the object, you have to identify the horizon line and you have to identify either one or two or three vanishing points. So, once you have done that you are ready to draw a perspective view, let us see how, one thing that I would want to tell you is whatever feature is there on the picture plane will appear in true dimensions in your perspective view. For example, this face of let us say a cube is right on the projection plane of the picture plane, so that will appear in two dimensions that is something that you need to keep in mind. Draw two projections vertically downward, get the height and this is what you will see in your perspective view, this face front view like so, now things become little interesting, if you look at this edge where would it vanish, if you look at this edge the corresponding image in the perspective view would be like so, if you look at n h far away, if you look at an object far away along this edge that would be vanishing over here. Likewise if you look at this edge it will start from here and objects far away along this edge that will be vanishing or they will be vanishing there. If you look at the bottom edge if you start from here, if you look at the bottom edge edge below this that will be vanishing again along this direction. So, in a sense what you have done is you have identified the three directions along which the edges are going to be vanishing or the objects are going to be vanishing along those edges. Now, follow this very carefully in the top view this is what my sight ray is that allows me to see that vertex, this ray intersects the projection plane or the picture plane here. I take the vertical projection to get the corresponding image of that intersection in the front view. So, the corresponding image of this vertex on this edge on the top edge of the cube will be here. Likewise if I look at this vertex here this ray intersects the picture plane over here at this point I draw the vertical projection and this is the corresponding image of that vertex in the perspective view. What is this edge the back edge this edge the edge on the left this one the edge on the right, but on the top face this guy here the bottom edge the edge on the right, but the bottom face and this. So, I will tell you about that. So, this is a one point perspective. So, I will tell you about two points and three points maybe later. So, what I have drawn is a single point perspective by that I mean that you have a single vanishing point and to draw that you have to keep two things in mind. Number one at least one face of the object that should be coincident with the picture plane or the projection plane not a vertex, but a single line or single face in the top view and of course, you have to have one vanishing point. So, if you are here and if you look at the object along one of the lines which is perpendicular to this perpendicular to the projection plane that ray is going to be hitting the horizon line over here that would be your vanishing point single vanishing point. How do you take the stationary point that is a choice. For example, I am stationed here I am looking at the entire class I will get one view I am stationed at a different position now I am looking at again the entire class I will get a slightly different view and if I get stationed here I will get a different view and do not ask me to go out. So, station point is like a parameter so it is usually specified in other words it is a choice should I go over this once again start with a blank sheet stay with me and be alert start with a blank sheet. Do not worry about that may be it will be a nice idea for you to work this out on your sketch planes or sketch books while I am going to this once again that is the top view this is the profile view profile view of the front view because the height is going to be the same both yeah missing this is a pictorial view that you are drawing this is something very similar to isometric view that you are drawing pictorial view just single view. So, given all these parameters how would the object look like to you in three dimensions are you not missing one no you just need the sight information from the top view and the height information from the profile view. So, essentially you have you get the three coordinates ready ready here we go start with the picture plane p p place the cube in top view in such a way that one of the edges is lying over the picture plane it is coincident with the picture plane. Step one Step two figure out where you are stationed in the top view just choose any random point step three in the front view or the profile view choose the ground line it could be either above the station point or below the station point does not really matter for now let us say it is above the station point. So, once again the station point is the one that you see in the top view. So, keep that in mind draw the profile view of the object on the ground line single cube figure out what your height is 56, 57, 58. If you are standing here this is where your horizon line should be the line of the eye once you have the horizon line you are ready to start making the perspective view. Once again keep in mind that any feature of the object in top view that is lying on the picture plane will appear in true dimension in the perspective view keep that in mind what is your height what is your height 62 sure. So, if you are stationed here and if you are not scaling your height your horizon is going to be 62 minus whatever your dimension whatever this dimension is alright. Let us draw the front face because we know that is going to be in true dimensions that is the vanishing point once again if you look at an object far away along this direction. So, this ray which is parallel to this edge over here of the object will be hitting the horizon line over here and that will become your vanishing point alright. So, get the true shape stay with me stay with me get this face in true shape extend a ray from this vertex towards the vanishing point extend another ray from this vertex towards the vanishing point the third ray from this vertex towards the vanishing point. So, in a sense the three edges of this cube are going to be vanishing along these directions and they are going to be converging towards the vanishing point. Let us use the sight information look at the vertex in top left in top view this ray is going to be intersecting the picture plane over here take the projection of this intersection on this edge. So, this is the image of this vertex in the perspective view likewise the vertex on top right this ray intersects the picture plane here get the projection of this this point is the image of this vertex in the perspective view and this point is the image of that vertex on the bottom edge of the cube and finish the cube. Let us say you have another cube let us say you have another cube Mishraji do you need some water double up double up you know it is not your fault it is not your fault I must be reminds me of my C S 101 days when I was taking the first year course in computer science. I was taking this course on C S 101 I guess I was being taught FORTRON by professor D. M. Thandere and it was not very nice day quite hot and we were actually sitting the p c section auditorium we have this nice auditorium there and I was in the second range and usually that is never happened with me except for that one incident where my eyes felt heavy and I was like and when the class was over and you know professor D. M. Thandere was just here and he could have a very nice view of me and I was like and after the class ended I was still like this and when somebody did this to me I woke up and I felt the stare. So, it happens so I do not blame you guys. So, imagine that we have another cube imagine that we have another cube of which the faces slightly behind the picture plane not on the picture plane but slightly behind the picture plane. What do you do? How do you get the height information? So, what you do is project that face of the edge on the picture plane you know that that will be in two dimensions you see that profile view on the right get that face in two dimensions. Get the three edges of this cube vanish and converge at v p use the sight information use the sight information this guy insects over here take the projection down that would be hitting one of those edges over there. Likewise use the sight information see this vertex from the station point get the intersection point project that downward and that would be hitting over here and this face would actually be your perspective face corresponding that object. Once again if the features of an object are not on the picture plane to get the height information project the feature of the object on the picture plane like. So, you know that this face is going to be in true shape it is going to be having two dimensions get the verticals down get the height information from the right draw that face in two dimensions draw this face in two dimensions let the three edges of that cube vanish at the vanishing point or towards the vanishing point. You would know that these two vertices they will have to lie on these two rays once you know that start working with the sight information use the top view look at this vertex this ray is going to be hitting the picture plane over here take that projection come down this is the image this point is the image of this vertex here. Likewise look at this vertex get the intersection point take the projection downward this point is the image of this point in the perspective once you have this point this point you would have the corresponding points on the bottom two edges you complete the face yeah we can fine stay with me stay with me and the rest is straight forward rest is straight forward look at that vertex on the left get its projection down look at this vertex on the left get the intersection point get its projection down and complete this cube like this straight forward once you once you understand how to construct straight forward it is not very difficult another example. So, this how the perspective of this cube looks this how the perspective of that cube looks and if you observe all these edges all these edges they tend to converge to a single vanishing point there how about on the right a cube a little far away from the projection plane do the same thing project for the faces on to the picture plane get the true face of this cube draw edges that converge towards the vanishing point use the site information project the intersection points get the perspective of the face of this face of the cube and follow the same procedure and finish the cube art is boring isn't it or maybe not. So, once you practice you will you will probably get a little more excited questions how many of you guys are with me it is pretty nice. So, let us draw a table let us draw a table in one point perspective the top view is given the profile view is given stay with me stay with me and some dimensions are given. So, do not worry about the dimensions once you have this information let us start I would just want you to observe I will go mute I will just want you guys to observe I will go slow shall I may I here you go before I go mute I will also explain why this is the vanishing point again if I am stationed over here if I am stationed over here and if I am looking at an object far away along this direction. So, this point would be my vanishing point on the horizon line and this ray from the station point that is again top view will be parallel to that edge of the object single point perspective of a table there you go keep your eyes on the screen there you go once again come after the mix and mix is this art not yet not yet, but is this going is this giving you a realistic view for table this is not isometric definitely are you getting a realistic view. So, just follow those little guidelines to draw a single point perspective view and practice in your host rooms before you leave wait wait wait wait before you leave in a single point perspective of course, you have a single vanishing point make sure that you have at least one face of the object parallel to the projection plane one face of the object parallel to the projection plane in the top view otherwise you would not get it right. So, this guy has to be parallel to the projection plane of the picture plane. So, if you have questions I am here otherwise